In this work, we study a novel query type, called top-<i>k,m</i> queries. Suppose we are given a set of groups and each group contains a set of attributes, each of which is associated with a ranked list of tuples, with ID and score. All lists are ranked in decreasing order of the scores of tuples. We are interested in finding the best combinations of… (More)
A well known theorem of Delmotte is that Gaussian bounds, parabolic Harnack inequality, and the combination of volume doubling and Poincaré inequality are equivalent for graphs. In this paper we consider graphs for which these conditions hold, but only for sufficiently large balls, and prove a similar equivalence.